Because the range of human hearing is bounded (nominally between 20
and 20 kHz), spectral components of a signal outside this range are
not audible. Therefore, when the solution to a differential equation
is to be considered an audio signal, there are frequency regions over
which convergence is not a requirement.

Instead of pointwise convergence, we may ask for the following two
properties:

Superposition holds for all linear partial differential equations with
constant coefficients (linear, shift-invariant systems [452]).
We need this condition so that errors in the inaudible bands do not
affect the audible bands.
Inaudible errors are fine as long as they do not grow so large that
they cause numerical overflow. An example in which this ``bandlimited
design'' approach yields large practical dividends is in
bandlimited interpolator design (see §4.4).